Re: [isabelle] Nominal2 fails on Datatypes with Lists

Dear Vincent,

Sorry, I should have seen this problem earlier. While the datatype package acquired the possibility to have nested datatypes where you can define

datatype ty = TRecord ‹ty list›

the Nominal2 package is still from a time where this was not possible. This means you would have to write something like this

      ty = TRecord ty_list
  and ty_list = Nil2
              | Cons2 ty ty_list

Unfortunately this means you define a "copy" of the list-datatype and you would have to reprove the facts you need for this copy.

Hope this helps,
From: Jackson, Vincent (Data61, Kensington NSW) <Vincent.Jackson at>
Sent: 17 October 2019 23:44
To: Urban, Christian <christian.urban at>; cl-isabelle-users at <cl-isabelle-users at>
Subject: Re: Nominal2 fails on Datatypes with Lists

A small theory that produces the error is

theory SmallLang
  imports Nominal2.Nominal2

nominal_datatype ty = TRecord ‹ty list›


the typevar was just an

atom_decl typevar

but this seems to be unrelated to the error.

I'm using the AFP Isabelle2019 version of Nominal2, if that helps.


On Tue, 2019-10-15 at 10:46 +0000, Urban, Christian wrote:
Dear Vincent,

I have to check what is going on. Would you be able top send me a slimmed-down theory where I can see what the problem is?

Also what is typevar in the TVar constructor?

From: cl-isabelle-users-bounces at<mailto:cl-isabelle-users-bounces at> <cl-isabelle-users-bounces at<mailto:cl-isabelle-users-bounces at>> on behalf of Jackson, Vincent (Data61, Kensington NSW) <Vincent.Jackson at<mailto:Vincent.Jackson at>>
Sent: 15 October 2019 03:20
To: cl-isabelle-users at<mailto:cl-isabelle-users at> <cl-isabelle-users at<mailto:cl-isabelle-users at>>
Subject: [isabelle] Nominal2 fails on Datatypes with Lists

Hello All,

I have been recently experimenting with Nominal2<;;sdata=8dL9LedsVKotsVQVSNab%2F2vu6ekR%2BDTHC%2BEnhZ%2BRC7U%3D&amp;reserved=0><>;, but have run into a problem with lists in datatypes.

The datatype

nominal_datatype ty

  = TRecord ‹ty list›

  | TVar typevar

fails with

Proof failed.

 1. ⋀x. TRecord_raw (map (permute p_) (- p_ ∙ x)) = TRecord_raw x

The error(s) above occurred for the goal statement⌂:

p_ ∙ TRecord_raw = TRecord_raw

presumably because the automation does not know (or use) the fact that ‹map (permute p) xs = p ∙ xs›.
Further, although I can prove the lemma, I am unsure how (or if it is possible) to 'inject' the fact into the automation.

Any advice on how to proceed would be appreciated.

Thank you,
Vincent Jackson

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